Boundedness of Solutions of a Quasi-periodic Sublinear Duffing Equation Citation： Yaqun PENG,Xinli ZHANG,Daxiong PIAO.Boundedness of Solutions of a Quasi-periodic Sublinear Duffing Equation[J].Chinese Annals of Mathematics B,2021,42(1):85~104 Page view： 113        Net amount： 70 Authors： Yaqun PENG; Xinli ZHANG;Daxiong PIAO Foundation： This work was supported by the National Natural Science Foundation of China (Nos.,11571327, 11971059). Abstract： The authors study the Lagrangian stability for the sublinear Duffing equations ddot{x}+e(t)|x|^{\alpha-1}x=p(t) with 0<\alpha<1,where e and p are real analytic quasi-periodic functions with frequency omega. It is proved that if the mean value of e is positive and the frequency omega satisfies Diophantine condition, then every solution of the equation is bounded. Keywords： Hamiltonian system, Sublinear Duffing equation, Boundedness, Quasiperiodic solution, Invariant curve Classification： 34C11, 34D20, 37E40, 37J40 Download PDF Full-Text